As of this morning, GTK+ Git has initial touch event support for Broadway. The commit message by Red Hat's Alexander Larsson reads, "This seems to get something going on an ipad, but some events seem to get swallowed. For instance, window dragging doesn't work."
So the GTK3 Broadway back-end can now handle touch events through its HTML5-rendered interface, which Alexander then tested from an Apple iPad. This is nothing about native iOS integration but rather running GTK in a web-browser from touch-enabled mobile devices. GTK3 doesn't have any native iOS integration but if you're looking for an open-source multi-platform tool-kit that does, Qt 5.2 will likely be your best bet.
Broadway touch support along with other GTK improvements will be present in the next stable release, GTK 3.12, which will be out next March with GNOME 3.12.